WASHINGTON—Health and Human Services Secretary Kathleen Sebelius, who led the government's troubled rollout of the 2010 health-care law, will step down, her spokeswoman confirmed Thursday, capping a rocky five years in the Obama cabinet.

President Barack Obama was expected to announce on Friday that Mrs. Sebelius, 65 years old, will be succeeded by Sylvia Mathews Burwell, the director of the Office of Management and Budget,...